1. For the given transformation,T: R³ → R², T(x, y, z) = (3x-2z, 2y - z)->a) Find the standard matrix A for the linear transformation T.b) Use A to find the image of the vector v =(0,1,1). 2. Given the matrix A = [6] and P = [1find A5 using a diagonal matrix D = P-1 AP.

The standard matrix of a linear transformation T : R3 →R2 can be found by applying T to the standard…

Answered: 1. For the given transformation, T: R³…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Let W be the line y = x in R². (a) Find a unit vector u on W. (b) Consider the linear transformation T: R² R² that projects each vector orthogonally onto W. Calculate the matrix for T which is uu¹. (c) Use that matrix to calculate T (d) Draw the vector [] [4] T[A] the line W, and the projection T

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1. For the given transformation, T: R³ → R², T(x, y, z) = (3x-2z, 2y - z) -> a) Find the standard matrix A for the linear transformation T. b) Use A to find the image of the vector v = (0,1,1). 2. Given the matrix A = [6] and P = [1 find A5 using a diagonal matrix D = P-1 AP.